Extending standard proximal methods and their convergence analysis
to Bregman distances is not straightforward because some fundamental
properties of the Euclidean proximal operator no longer hold
for Bregman proximal operators.
An example is the Moreau decomposition
which relates the (Euclidean) proximal operators of a closed convex
function and its conjugate [1]}.
Another example is the simple relation between
the proximal operators of a function \(g\)  and
the composition with a linear function \(g(Ax)\) 
when \(AA^T\)  is a multiple of the identity;
see, e.g., [2]}, [3]}.
This composition rule is used in [4]}
to establish the equivalence between some well-known first-order proximal
methods for problem (REF ) with \(A=I\)  and with general \(A\) .
